Soundboard construction for stringed musical instruments

ABSTRACT

A soundboard for stringed musical instruments in which the soundboard is reinforced by a series of ribs spaced apart by a distance less than one-half the wave length of the vibration of the soundboard at the fundamental frequency of the highest note on the instrument scale.

United States Patent 1 1 Conklin, Jr.

- 1 Feb. 18,1975

1 1 SOUNDBOARD CONSTRUCTION FOR STRINGED MUSICAL INSTRUMENTS [75]Inventor: Harold A. Conklin, Jr., Cincinnati,

Ohio

[73] Assignee: D. H. Baldwin Company, Cincinnati,

Ohio

[22] Filed: Oct. 19, 1973 {21] Appl. N0.: 407,854

3,086,420 4/1963 Yamumoto 84/195 3,443,464 5/1969 Akag' 84/195 FOREIGNPATENTS OR APPLICATIONS 27,771 11/1910 Great Britain 84/195 PrimaryE.raminerLawrence R. Franklin Attorney, Agent, or FirmMelvi11e,Strasser, Foster & Hoffman [57] ABSTRACT A ndboard for stringed musicstruments in all in wh' the soundboard is reinforced by a series of ribsspaced apart by a distance less than one-half the wave 1e of thevibration h undboard a fundam frequency of hi st note on instrumentscale.

11 Claims, 2 Drawing Figures PATENTEI] FEB] 8l975 SOUNDBOARDCONSTRUCTION FOR STRINGED MUSICAL INSTRUMENTS BACKGROUND OF THEINVENTION This invention has to do with the soundboards for pianos andsimilar musical instruments, and relates more particularly to asoundboard construction having improved uniformity of frequencyresponse, improved and extended high frequency response, higherefficiency at higher frequencies, and improved tone quality.

In a piano the soundboard is the major sound radiating element. Normallythe soundboard is a thin wooden panel coupled mechanically to thestrings in ways wellknown to those skilled in piano building, so thatwhen the strings are struck by the hammers of the piano, the vibrationof the strings is transmitted to the soundboard. Piano soundboards arecustomarily constructed of quarter sawn softwood, the usual practicebeing to fabricate the soundboard by gluing a number of relativelynarrow quarter sawn strips together along their parallel edges with thegrain of the wood running parallel to the length of the strips. As thosefamiliar with industry practice will know, a perfectly quarter sawnstrip of wood is one having the grain line running exactly perpendicularto the surface of the strip when viewed in cross-section. In practice,quarter sawn wood may be allowed to have some angular deviation of thegrain from the perpendicular in order to minimize waste.

It is the usual practice to employ stiffening ribs fastened to thesurface of the soundboard opposite from the strings, the ribs extendingparallel to each other and positioned so as to have their longitudinalaxes at right angles to the direction of the grain of the soundboardstrips. The ribs themselves are usually made of quarter sawn softwoodwith the grain of the wood normally oriented in a direction lengthwiseof the ribs and hence at right angles to the grain direction of thesoundboard strip.

Soundboard ribs serve three basic purposes:

1. to stiffen the soundboard in a direction in which the soundboarditself (without the ribs) inherently lacks stiffness;

2. to add mechanical strength in a direction in which the soundboard isinherently weak; and

3. to help make soundboards more uniform in characteristics from one tothe other.

In conventional pianos the number and size of the ribs and the spacingbetween the ribs varies from one design to another within well-knowntypical limits. Generally, the number of ribs depends upon the size ofthe soundboard; the longer the soundboard the more ribs required. Thecross-sectional area of the ribs may vary, but generally will be in therange of between approximately 3.0 and 6.5 square centimeters along themid-section of each rib, the ribs usually being of maximum thickness intheir mid-section with their opposite ends tapered to be of lesserthickness. The spacing of the ribs, from centerline to centerline,normally varies moderately, both from rib to rib within a particularinstrument and also from one design to another. Generally speaking,however, the spacing varies over no greater range than fromapproximately centimeters to approximately 18 centimeters. The foregoingparameters are so prevalent as to constitute standard industry practice;and while individual designs may depart slightly from the foregoingcriteria, the amount of the deviation usually is so small that it can beignored in considering the basic performance of the soundboard.

In accordance with the present invention, it has been found that thenormal spacing of the ribs employed in conventional pianos producescertain undesirable effects on the frequency response of the soundboardwith the result that an important portion of the sound spectrumgenerated by the strings of the instrument is radiated with lowerefficiency and with less uniform efficiency than the remainder of thespectrum. Specifically, it has been found that the frequency response ofa conventional soundboard is deficient at high frequencies. In addition,the conventional rib construction re sults in non-uniformity in theinstrument scale. Varitions of efficiency in soundboard radiation willcause some notes or groups of notes to be less loud than others.

RESUME OF THE INVENTION.

In accordance with the present invention, it has been found thataltering the number, size and spacing of the reinforcing ribs produces amaterial improvement to the efficiency and uniformity of response of thesoundboard, particularly at the higher audio frequencies.

It has been found that if a soundboard strip is driven at one point thesound pressure level at some other point, such as the far end of thestrip, depends upon the transmission characteristics between the twopoints. In other words, if the sound radiating efficiency at a distantpoint of such a strip is to be uniform as the frequency is varied, thenthe transmission characteristic of the strip must be uniform. If thetransmission response is first measured for a soundboard strip withoutribs and then measured with conventional ribs added, i.e., ribs ofconventional size and spacing, it has been found that an undesirablealteration of the transmission response characteristics of the stripoccurs because of the addition of the ribs. The nature of thisalteration has been found to be similar to the effect produced by a lowpass mechanical filter in that attenuation of the higher frequenciesoccurs. The amount of such attenuation has been found to depend upon thenumber, spacing, and mass of the ribs. For rib arrays normally used onsoundboards of conventional design the attenuation effect is significantat frequencies within the normal keyboard range of the instrument.

An important criterion for determining the lowest frequency at whichsevere attenuation or frequency distortion occurs is the spacing of theribs. At the frequency at which the spacing of the ribs is equal toonehalf a vibrational wave length along the soundboard strip, asignificant attenuation in the transmission efficiency of the strip hasbeen found to occur. As the driving frequency is increased theattenuation also increases, although the response may increasetemporarily after a maximum of attenuation at the half-wave lengthfrequency has been passed.

In accordance with the invention, in order to'prevent undesirableattenuation of the higher frequencies, the spacing of the ribs(center-to-center distance between adjacent ribs) must be less thanone-half the wave length of the vibration of the soundboard in thedirection of the grain at the highest frequency of interest, which isusually the highest note on the instrument scale. In a conventionalpiano tuned to international standard pitch wherein the note A, the 49thnote of a standard 88 note piano keyboard, has a frequency of 440 Hz.,the highest fundamental scale frequency of interest is the 88th note onthe keyboard, which has a nomial frequency of 4,186 Hz. As will be knownto those familiar with piano design, inharmonicity and the resultingnatural stretch in tuning of the instrument normally make the highestnote slightly higher in frequency than 4,186 Hz., but, nevertheless,4,186 Hz. may be regarded as the highest standard reference scalefrequency.

In order to establish the proper rib spacing for a soundboard it isnecessary first to measure or otherwise determine the length of ahalf-wave of vibration on a soundboard strip in relation to thevibration frequency. This relationship may be determined eitherempirically, by measurement of propagation on an acutal soundboardstrip, or it may be calculated based on assumed or measured values forthe parameters of the strip. For typical soundboard wood, a half-wavelength in the direction of the grain at 4,186 Hz. will be about 6.35centimeters for a soundboard 0.635 centimeter (A inch) thick and about7.78 centimeters for a soundboard 0.953 centimeter inch) thick. Ribspacing must be significantly less than these values in order to haveuniform transmission response of a soundboard strip up to the highestscale frequency. The ribs must thus be spaced much closer together thanin a conventional soundboard construction.

Another factor affecting significantly the frequency response of thesoundboard is the cross-sectional area or mass of the ribs. In general,increasing the weight of the ribs causes significant attenuation tobeing at a lower frequency and causes total attenuation at a particularfrequency to be greater than for ribs of lesser mass. If additional ribsof standard size are used, the total weight of the soundboard and itstotal stiffness will be increased, and less than optimum performanceobtained. Consequently, in accordance with the invention it is desirableto employ ribs having reduced crosssectional width, so that the totalnet effective stiffness and mass of the soundboard assembly will remainthe same or nearly the same as for a well-designed soundboard ofconventional construction. It should be noted in particular that it isperferable to reduce the crosssectional width of the rib, rather thanits depth, when the number of ribs is increased. This is because thestiffness ofa rib is directly proportional to its width, but varies asthe cube of its depth. In addition, the natural vibrational frequenciesof a rib do not change if the width is reduced but, on the other hand,if the depth is varied, the vibrational frequencies are proportional tothe depth. Therefore, if the rib cross-section were to be reduced byreducing the depth of the rib rather than its width, as the number ofribs is increased, then both the net stiffness and the modal resonantfrequencies of the soundboard would be undesirably changed.Consequently, if the number of ribs is doubled as compared to aconventional soundboard construction, the width of each rib should bemade approximately one-half that of the original.

It may be noted that conventional soundboards do not necessarily haveall of the ribs equally spaced. Typically, spacing on a given soundboardmay be 1 1.5 centimeters at the treble end, increasing to perhapscentimeters or so at the bass end of the soundboard. It is not necessaryfor a soundboard constructed according to the teachings of thisinvention to have constant rib spacing, but rather the rib spacing mayvary over a percentage range similar to that of conventionalsoundboards, so long as the widest spacing is still less than one-halfwave length at the highest frequency for which uniform response of thesoundboard is desired.

DESCRIPTION OF THE DRAWINGS FIG. 1 is a bottom plan view of a soundboardconstructed in accordance with the present invention.

FIG. 2 is a sectional view taken along the line 2-2 of FIG. 1.

DESCRIPTION OF THE PREFERRED EMBODIMENT In order to determine thecritical rib spacing for any given frequency it is necessary to firstdetermine the length of a half-length of vibration on a soundboard stripin relation to the vibration frequency. Measurement on an actualsoundboard strip can be readily made using a narrow longitudinal sectionof the soundboard strip which acts as a transmission line. While thevibration of the soundboard as a whole is much more complex that that ofa narrow strip of the soundboard material, the vibrational behavior of anarrow strip is basically like that of the soundboard itself insofar aspropagation of vibrational energy in the direction of the soundboardstrips is concerned. Ignoring for the moment the effect of the ribs, thebehavior of the soundboard strips is basically similar, once the stripsare installed in the piano case, to that of a clampedclamped beam,because the ends of each strip are fixed solidly by adhesive to themassive sides of the piano case. As is well-known to those familiar withvibration technology, the natural frequencies of a clampedclamped beamare the same as those for a free-free beam, and are dependent upon theelastic modulus and density of the material of the beam and on itslength and thickness, and may be computed according to formulasavailable from standard textbooks on sound and vibration. lfa narrowstrip is driven in flexural or trans verse vibration at or near one endby a mechanical vibration generator and if the resulting vibration at ornear the opposite end of the strip is picked up by a min iatureaccelerometer and recorded as the driving frequency is varied throughthe audio frequency range, frequency response data .for the transmissioncharacteristic of the soundboard strip can be obtained. Standing wavesare present on the strip and may be recognized as alternate maxima andminima in the vibration intensity measured at successive points on thestrip. The distance between two adjacent points of minimum intensity atany particular transmission frequency represents a distance of one-halfwave length at that particular frequency. As the driving frequencyincreases, the wave length or distance between sucessive minimadecreases.

Alternatively, if the distance of one-half wave length is to becalculated, it is necessary to know the thickness, elastic modulus, anddensity of the strip material. It is not necessary to know the width ofthe strip because propagation of flexural vibrations lengthwise on sucha strip is basically independent of width.

The basic equation is:

The equation applies to an homogeneous strip of rectangularcross-section where h is the thickenss of the strip in centimeters,fisthe frequency in Hz., V is the velocity of propagation of longitudinalwaves in the material in centimeters per second, and M2 is the halfwavelength in centimeters.

In order to obtain values of )\/2 versus f, it is necessary to obtainthe correct value for V,, The equation for longitudinal velocity ofpropagation is:

VL /p)1l2 where E is the Youngs or elastic modulus of the mate rial indynes per square centimeter, and p is the density of the material ingrams per cubic centimeter.

If typical valves of E and p are known, the value for V may be readilyobtained. If E and p are not known for the wood being used, they may bedetermined by known methods. However, dynamic methods of obtaining Eshould be used rather the the method of static loading because the twomethods do not give the same answer, and because the vibrational methodgives the result that is applicable to pinao soundboards, sincesoundboard performance under vibration rather than under static loadingis the thing of interest. p may be readily determined by dividing theweight of a typical sample of the material in grams by its volume incubic centimeters.

Piano soundboards normally are fabricated of spruce or a similar woodwhich is relatively light in weight, a typical value for the density ofsuitable wood being about 0.4 grams per cubic centimeter. A typicalsoundboard may have a thickness in the range of about 0.6 to 1.0centimeters, exclusive of the ribs, and may have a length and widthalmost as great as the length and width of the piano case itself. For alarge grand piano the length of the soundboard may be as much as 210centimeters and the width 150 centimeters.

In a typical example in which the soundboard strip has a thickness of0.953 centimeter, a density of 0.4 grams per cubic centimeter, and anelastic modulus of (1.38) l0 dynes per square centimeter, the value ofone-half wave length at a frequency of 4,186 I-Iz; would be 7.78centimeters (about 3.06 inches). In a soundboard strip having the samephysical properties except being only 0.635 centimeter thick, thehalf-wave length value would be 6.35 centimeters (about 2.5 inches).These strip thicknesses represent approximately the extreme values ofsoundboard thickness encountered in conventional panios. It should bepointed out in connection with soundboard thickness that it is a commonpractice to taper the edges of the soundboard, the tapered portionusually being confined to a peripheral band around the outside edges ofthe soundboard which may be on the order of to 18 centimeters wide. Asused therein, the soundboard thickness is the value applying to thecentral portion of the soundboard and it is the thickness which is usedto calculate the spacing of all of the ribs.

It follows from the principles taught herein that in order to avoidsignificant distortion and non-uniformity of frequency response of thesoundboard within the frequency range of the basic scale tones, it isnecessary to have the distance from the centerline of one rib to thecenterline of the next rib less than about 7.78 centimeters for asoundboard 0.953 centimeter thick, and less than about 6.35 centimetersfor a soundboard 0.635 centimeter thick. Even smaller rib spacing may bedesirable in order to avoid response perturbations within the entirehigh frequency audio range, which extends above the highest pianofundamental scale frequency. It may be noted from the half wave lengthformula that the critical rib spacing varies in inverse proportion tothe square root of frequency. It follows, therefore, that to double thefrequency would require the rib spacing to be reduced by a factor of l/VTMinimum rib spacing is governed primarily by practical designconsiderations. Excessive reduction in rib spacing would only increasethe cost and complexity of constructing the soundboard without asignificant improvement in the tonal result.

As to the width of the ribs themselves, if it is desired to employ alarge number of narrower ribs, keeping the same rib depth, and if it isdesired to keep the net resulting stiffness of the soundboardessentially the same, the numerical ratio between the width of the ribs(W) and the spacing from the center of one rib to the center of the nextrib (D) should be kept constant. This ratio may be expressed by thefraction W/D. By way of example, if it is desired to redesign aconventional soundboard using ribs 2.5 centimeters wide and spaced 14centimeters on centers so as to have a new spacing of 5 centimeterscenter-to-center, while maintaining the same net stiffness per unitlength of the soundboard, the new value of rib width would be selectedto retain the same value of W/D as in the old soundboard. For the oldsoundboard W/D 2.5/14 0.1786; therefore the new rib width would be W=(5) (0.1786) 0.892 centimeter.

It is not necessary for a soundboard in accordance with the presentinvention to have constant rib spacing, as long as the widest spacing isless than one-half wave length at the highest frequency for whichuniform response of the soundboard is desired. Generally speaking, thespacing may vary over a percentage range comparable to that ofconventional soundboards, which may vary in spacing from about 1 1.5centimeters at the treble end to about 15 centimeters at the bass end ofthe soundboard.

FIG. 1 illustrates a soundboard, indicated generally at 1, designedaccording to the principles of the invention. The soundboard is composedof a plurality of strips 2 formed from quarter sawn lumber having thegrain direction extending lengthwise of the strips. This is a soundboardfor a concert grand piano having thirty nine ribs 3 extending at rightangles to the length of the strips 2, the ribs being spaced apart from5.08 to 6.02 centimeters. The thickness of the soundboard is between0.874 and 0.953 centimeter. The nominal elastic modulus of thesoundboard strips is (1.38) 10 dynes per square centimeter and thedensity is 0.4 grams per cubic centimeter. Each rib is approximately1.12 centimeters in width. The soundboard was designed to replace aconventional soundboard having 17 ribs each of which is 2.54 centimeterswide.

While the foregoing example is exemplary of a soundboard constructed inaccordance with the invention, it is possible to vary the width of theribs and their number consistent with good design practice, includingvarying the width of the ribs from rib to rib. A salient considerationis the maintenance of the desired tonal characteristics of theinstrument, including improved efficiency and uniformity of response ofthe soundboard at higher audio frequencies.

It has been found that piano soundboards constructed in accordance withthe principles disclosed herein, namely, soundboards having the ribsspaced and sized according to the criteria given, have improveduniformity of frequency response, improved and extended high frequencyresponse, higher efficiency at higher frequencies, and improved tonequality. Such instruments may employ softer hammers than conventionalpianos, while .still radiating sufficient sound energy at highfrequencies. Soft hammers are advantageous because such hammers allowimproved quality of tone and improved tone-to-noise ratio.

Modifications may be made in the invention without departing from itsspirit and purpose. Numerous variations in the design criteria havealready been discussed, and others will undoubtedly occur to the skilledworker in the art upon reading this specification. For example, whilethe soundboard strips may be formed from quarter sawn lightweight wood,the principles of the invention are applicable to other materialscapable of forming a suitable soundboard, such as a laminated soundboardstructure. While the invention is directed primarily to standard pianoshaving 88 notes in the scale, the principles are also applicable toinstruments having a greater or lesser number of notes, within practicallimits of sound piano design.

The embodiments of the invention in which an exclusive property orprivilege is claimed are defined as follows:

1. In a musical instrument having a plurality of strings defining thescale of the instrument, a soundboard having a series of spaced apartreinforcing ribs secured thereto, adjacent ribs throughout said seriesof ribs being spaced apart by a distance between their centerlines whichis less than one-half the vibrational wave length of the soundboard atthe fundamental scale frequency of the highest note on the scale of theinstrument, the numerical ratio between the cross-sectional widths ofthe ribs and the distance between the centerlines of adjacent ribs beingmaintained essentially constant irrespective of the number of ribsemployed.

2. The musical instrument claimed in claim 1 wherein said soundboardcomprises a plurality of elongated strips juxtaposed in side-by-siderelation, and wherein said ribs extend in a direction at right angles tothe lengths of said strips.

3. The musical instrument claimed in claim 2 wherein said soundboardstrips comprise quarter sawn wood with the grain direction extendinglengthwise of the strips and at substantially right angles to thesurfaces of the strips.

4. The musical instrument claimed in claim 3 wherein said ribs areformed of quarter sawn wood having the grain extending lengthwise of theribs and at substantially right angles to the surfaces of the strips.

5. The musical instrument claimed in claim 1 wherein said soundboard hasa thickness of from 0.635 centimeter to 0.953 centimeter.

6. The musical instrument claimed in claim 5 wherein said adjacent ribsare spaced apart by a distance of less than 7.78 centimeters when saidsoundboard has a thickness of 0.953 centimeter, and a distance of lessthan 6.35 centimeters when the soundboard has a thickness of 0.635centimeter.

7. The musical instrument claimed in claim 6 wherein the fundamentalscale frequency of the highest note on the scale of the instrument isnominally 4,186 Hz.

8. A soundboard for use in a piano having a plurality of stringsdefining the scale of the instrument, said soundboard having a series ofspaced apart reinforcing ribs secured thereto, adjacent ribs beingspaced apart by a distance between their respective centerlines which isless than one-half the vibrational wave length of the soundboardmaterial in accordance with the equation x 2 =(1rh VA V3 wherein h isthe thickness of the soundboard in centimeters,fis the frequency in Hz.of the highest note on the scale of the instrument, V is the velocity ofpropagation of longitudinal waves in the soundboard material incentimeters per second, computed in accordance with the equation Vt(ta/p) wherein E is the Youngs or elastic modulus of the soundboardmaterial in a direction at right angles to the longitudinal axes of thereinforcing ribs in dynes per square centimeter, and p is the density ofthe material in grams per cubic centimeter, and wherein M2 is thehalf-wave length in centimeters, the ratio of rib width to rib spacingbeing maintained essentially constant irrespective of the number of ribsemployed.

9. The piano soundboard claimed in claim 8 wherein h is from 0.635centimeter to 0.953 centimeter.

10. The piano soundboard claimed in claim 9 wherein M2 is less than 7.78centimeters when h equals 0.953 centimeter, and M2 is less than 6.35centimeters when h equals 0.635 centimeter.

11. The piano soundboard claimed in claim 10 whereinf is nominally 4,186Hz.

1. In a musical instrument having a plurality of strings defining thescale of the instrument, a soundboard having a series of spaced apartreinforcing ribs secured thereto, adjacent ribs throughout said seriesof ribs being spaced apart by a distance between their centerlines whichis less than one-half the vibrational wave length of the soundboard atthe fundamental scale frequency of the highest note on the scale of theinstrument, the numerical ratio between the cross-sectional widths ofthe ribs and the distance between the centerlines of adjacent ribs beingmaintained essentially constant irrespective of the number of ribsemployed.
 2. The musical instrument claimed in claim 1 wherein saidsoundboard comprises a plurality of elongated strips juxtaposed inside-by-side relation, and wherein said ribs extend in a direction atright angles to the lengths of said strips.
 3. The musical instrumentclaimed in claim 2 wherein said soundboard strips comprise quarter sawnwood with the grain direction extending lengthwise of the strips and atsubstantially right angles to the surfaces of the strips.
 4. The musicalinstrument claimed in claim 3 wherein said ribs are formed of quartersawn wood having the grain extending lengthwise of the ribs and atsubstantially right angles to the surfaces of the strips.
 5. The muscialinstrument claimed in claim 1 wherein said soundboard has a thickness offrom 0.635 centimeter to 0.953 centimeter.
 6. The musical instrumentclaimed in claim 5 wherein said adjacent ribs are spaced apart by adistance of less than 7.78 centimeters when said soundboard has athickness of 0.953 centimeter, and a distance of less than 6.35centimeters when the soundboard has a thickness of 0.635 centimeter. 7.The musical instrument claimed in claim 6 wherein the fundamental scalefrequency of the highest note on the scale of the instrument isnominally 4,186 Hz.
 8. A soundboard for use in a piano having aplurality of strings defining the scale of the instrument, saidsoundboard having a series of spaced apart reinforcing ribs securedthereto, adjacent ribs being spaced apart by a distance between theirrespective centerlines which is less than one-half the vibrational wavelength of the soundboard material in accordance with the equation lambda/2 ( pi h VL4 Square Root 3f)1/2 wherein h is the thickness of thesoundboard in centimeters, f is the frequency in Hz. of the highest noteon the scale of the instrument, VL is the velocity of propagation oflongitudinal waves in the soundboard material in centimeters per second,computed in accordance with the equation VL (e/ Rho )1/2 wherein E isthe Young''s or elastic modulus of the soundboard material in adirection at right angles to the longitudinal axes of the reinforcingribs in dynes per square centimeter, and Rho is the density of thematerial in grams per cubic centimeter, and wherein lambda /2 is thehalf-wave length in centimeters, the ratio of rib width to rib spacingbeing maintained essentially constant irrespective of the number of ribsemployed.
 9. The piano soundboard claimed in claim 8 wherein h is from0.635 centimeter to 0.953 centimeter.
 10. The piano soundboard claimedin claim 9 wherein lambda /2 is less than 7.78 centimeters when h equals0.953 centimeter, and lambda /2 is less than 6.35 centimeters when hequals 0.635 centimeter.
 11. The piano soundboard claimed in claim 10wherein f is nominally 4,186 Hz.